Terms of the deal weren't disclosed.
Evans, who played collegiately at Memphis, split last season between the New Orleans Pelicans and Sacramento Kings. The 6-foot-6 guard averaged 10.3 points, 3.4 rebounds and 3.1 assists in 40 games.
The 27-year-old has averaged 16.1 points. 4.8 rebounds and 5.1 assists over his eight-year NBA career. He was named the 2009-10 NBA rookie of the year.
Grizzlies general manager Chris Wallace said in a release that "Tyreke has proven his talent throughout his NBA career as both a scorer and playmaker, and we are pleased to add a player of his versatility to the Grizzlies."